Statistics Fundamentals • Topic 6 of 6

Interquartile Range

The interquartile range (IQR) is the spread of the middle 50% of the data: IQR = Q3 − Q1. Because it ignores the extreme quarters, the IQR is resistant to outliers and is the preferred measure of spread for skewed data — unlike the range, which the extremes dominate. A common SAT use is comparing the consistency of two data sets: the one with the smaller IQR is more tightly clustered in the middle. The IQR is also used to flag outliers. The skill is finding Q1 and Q3 correctly, then subtracting.

✅ Solved examples

1. Given Q1 = 10 and Q3 = 20, find the IQR.
IQR = Q3 − Q1 = 20 − 10 = 10.
2. Find the IQR of 2, 4, 6, 8, 10, 12.
Q1 = 4, Q3 = 10, so IQR = 6.
3. A data set has Q1 = 15 and Q3 = 35. IQR?
35 − 15 = 20.
4. Which is more consistent: IQR 5 or IQR 12?
A smaller IQR means tighter spread, so the set with IQR 5.

✏️ Practice — try these, take hints as needed

1. Given Q1 = 8 and Q3 = 23, find the IQR.
IQR = Q3 − Q1.
23 − 8.
—
15.
2. Find the IQR of 3, 6, 9, 12, 15, 18.
Q1 = 6, Q3 = 15.
Subtract.
—
9.
3. A data set has Q1 = 20 and Q3 = 50. IQR?
Q3 − Q1.
50 − 20.
—
30.
4. Which data set is more spread out: IQR 4 or IQR 11?
Larger IQR = more spread.
11 > 4.
—
The one with IQR 11.
5. Find the IQR of 1, 2, 3, 4, 5, 6, 7, 8.
Q1 = 2.5, Q3 = 6.5.
Subtract.
—
4.

📝 Topic test — 8 questions

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